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Efficient and exact sampling of simple graphs with given arbitrary degree sequence
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Rapallo, Fabio, Del Genio, Charo I., Kim, Hyunju, Toroczkai, Zoltán and Bassler, Kevin E. (2010) Efficient and exact sampling of simple graphs with given arbitrary degree sequence. PLoS ONE , Vol.5 (No.4). Article no. e10012. doi:10.1371/journal.pone.0010012 ISSN 1932-6203.
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Official URL: http://dx.doi.org/10.1371/journal.pone.0010012
Abstract
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large , and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | PLoS ONE | ||||
| Publisher: | Public Library of Science | ||||
| ISSN: | 1932-6203 | ||||
| Official Date: | 2010 | ||||
| Dates: |
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| Volume: | Vol.5 | ||||
| Number: | No.4 | ||||
| Page Range: | Article no. e10012 | ||||
| DOI: | 10.1371/journal.pone.0010012 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) |
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